Best Known (61−24, 61, s)-Nets in Base 8
(61−24, 61, 256)-Net over F8 — Constructive and digital
Digital (37, 61, 256)-net over F8, using
- 3 times m-reduction [i] based on digital (37, 64, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 32, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 32, 128)-net over F64, using
(61−24, 61, 300)-Net in Base 8 — Constructive
(37, 61, 300)-net in base 8, using
- 1 times m-reduction [i] based on (37, 62, 300)-net in base 8, using
- trace code for nets [i] based on (6, 31, 150)-net in base 64, using
- 4 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- 4 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- trace code for nets [i] based on (6, 31, 150)-net in base 64, using
(61−24, 61, 347)-Net over F8 — Digital
Digital (37, 61, 347)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(861, 347, F8, 24) (dual of [347, 286, 25]-code), using
- 24 step Varšamov–Edel lengthening with (ri) = (1, 23 times 0) [i] based on linear OA(860, 322, F8, 24) (dual of [322, 262, 25]-code), using
- trace code [i] based on linear OA(6430, 161, F64, 24) (dual of [161, 131, 25]-code), using
- extended algebraic-geometric code AGe(F,136P) [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
- trace code [i] based on linear OA(6430, 161, F64, 24) (dual of [161, 131, 25]-code), using
- 24 step Varšamov–Edel lengthening with (ri) = (1, 23 times 0) [i] based on linear OA(860, 322, F8, 24) (dual of [322, 262, 25]-code), using
(61−24, 61, 29435)-Net in Base 8 — Upper bound on s
There is no (37, 61, 29436)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 12 264844 669689 219390 655537 511996 785545 889215 864311 893308 > 861 [i]